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Abstract

A monolithically integrated asymmetric graded index (GRIN) or step-index (GRIN) mode converters for microphotonic waveguides are proposed and described. The design parameters and tolerances are calculated for amorphous silicon (a-Si) couplers integrated with silicon-on-insulator waveguides. The GRIN and step-index couplers operate over a wide wavelength range with low polarization dependence, and the lithographic resolution needed is only ±1 μm. Finally, experimental results are presented for a single layer 3 μm thick step-index a-Si coupler integrated on a 0.8 μm thick SOI waveguide. The measured variation of coupling efficiency with coupler length is in agreement with theory, with an optimal coupling length of 15 μm for this device.

(a) The field distribution in a full quadratic index waveguide (n0 = 3.405, x0 = 8.23 μm), for mode expansion coefficients that alternate in phase by π (solid curve) and 2π. (b) The corresponding field distribution in a semi-infinite quadratic index waveguide, for modes that alternate in phase by 2π (solid curve) and π (dashed curve).

The index profiles (shaded regions) and the lowest order electric field TE mode profiles for (a) a full quadratic index waveguide, (b) a truncated quadratic index waveguide, (c) an optimized asymmetric-GRIN coupler on a 0.5 μm Si waveguide, and (d) a single layer step-index coupler on a 0.5 μm Si waveguide.

The modal wave vectors βv for TE polarized light in the full quadratic index waveguide, the truncated quadratic index waveguide, and the optimized asymmetric-GRIN coupler on a 0.5 μm Si waveguide shown in Fig. 3. The dashed curved represents a linear extrapolation of the wave vector dependence on mode number.

The variation of coupling efficiency on coupler length for an optimized asymmetric-GRIN coupler on a 0.5 μm Si waveguide (solid curve), and a single layer step-index coupler on a 0.5 μm Si waveguide (dashed curve). The calculations are for TE polarized light.

(a) Cross-section of the fabricated asymmetric-GRIN single layer coupler structure, and (b) a scanning electron microscope (SEM) view of the etched waveguide facets showing the 3 μm deposited a-Si layer on the 0.8 μm high Si ridge waveguides, and the outline of the SiO2 window that defines the coupler length.

The variation of the measured output power with coupler length for a 3 μm thick single layer a-Si coupler integrated with a 0.8 μm SOI waveguide as described in the text. The solid curve is the calculated coupling efficiency assuming TE polarized light and an a-Si refractive index of n=3.365.

Tables (2)

Table 1. Mode expansion coefficients and coupling efficiencies a for the truncated quadratic index and GRIN coupler structures in Fig. 3(b) and 3(c). The calculated coefficients are for TE polarized light.